Are two Nakayama algebras with a linear quiver derived equivalent if and only if they have the same coxeter polynomial?
Derived categories of Nakayama algebras appear in interesting contexts (see for example https://www.sciencedirect.com/science/article/pii/S0001870813000182 )and it would be surprising if the question has a positive answer.
Note that derived equivalent algebras always have the same coxeter polynomial but the other direction is false in general.
